TY - JOUR
T1 - Translation operator and maximal function for the (k,1)-generalized Fourier transform
AU - Ben Saïd, Salem
AU - Deleaval, Luc
N1 - Publisher Copyright:
© 2020 Elsevier Inc.
PY - 2020/11/1
Y1 - 2020/11/1
N2 - In this paper we study a translation operator associated with the n-dimensional (k,1)-generalized Fourier transform, where k is a multiplicity function for the Dunkl operators. In particular, we prove that the translation is a positivity-preserving operator acting on a suitable space of radial functions on Rn. We then use it to define a Hardy-Littlewood type maximal operator, where weak-type (1,1) and strong-type (p,p) estimates for the maximal operator are established with a precise behavior in n and k.
AB - In this paper we study a translation operator associated with the n-dimensional (k,1)-generalized Fourier transform, where k is a multiplicity function for the Dunkl operators. In particular, we prove that the translation is a positivity-preserving operator acting on a suitable space of radial functions on Rn. We then use it to define a Hardy-Littlewood type maximal operator, where weak-type (1,1) and strong-type (p,p) estimates for the maximal operator are established with a precise behavior in n and k.
KW - Dunkl's intertwining operator
KW - Generalized Fourier transform
KW - Generalized translation operator
KW - Hardy-Littlewood type maximal operator
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U2 - 10.1016/j.jfa.2020.108706
DO - 10.1016/j.jfa.2020.108706
M3 - Article
AN - SCOPUS:85088269633
SN - 0022-1236
VL - 279
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
IS - 8
M1 - 108706
ER -